Let
y ------> the amount earned
x ----> the number of hours worked
In this problem we have a direct variation
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx
where
k is the constant of proportionality
k=y/x
In this problem the value of k is hourly rate
so
we have
For y=$90 -------> x=5 hours
substitute
k=90/5
k=$18 per hour
substitute in the linear equation
y=18x
so
Part 1) What is the meaning of the 18 that appears in the table?
18 is the hourly rate ( amount earned by a one hour of work)
Part 2) Explain how Lin used this table to solve the problem.
using the table
For x=8 hours
the value of y=$144
Verify with the equation
y=18x
y=18(8)=144 -----> is ok
Part 3) At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work.
For x=3 hours
substitute in the equation
y=18x
substitute the value of x
y=18(3)=$54
For x=2.1 hours
y=18(2.1)=$37.8
What is the largestNumber of these wooden Els that can be packed in a box that is 2 cm x 4 cm x 6 cm
The largest number of the wooden Els with it's total surface area that can be packed in the 2cm×4cm×6cm box is 2 wooden Els.
Total Surface Area of Solid ShapesIn finding the total surface area of a solid cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) and use the formula, SA=2(lw+lh+hw), to find the surface area.
For the box, l=2cm, w=4cm and h=6cm
total surface area of box=2(2×6+2×4+6×4) cm square units
total surface area of box=2(44) cm square units
total surface area of box=88cm square units
For the top cuboid of the wooden El, l=3cm, w=1cm and h=2cm
total surface area of top El cuboid=22cm square units
For the bottom cuboid of the wooden El, l=1cm, w=1cm and h=2cm
total surface area of bottom El cuboid=10cm square units
total surface area of the El=32cm square units
(88cm²/32cm²)=2.75
This implies that only two(2) whole Els with total surface area of 32cm² can be packed in the box.
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Admission to a state fair is $10, and each ride ticket costs $2.50. Write an en
EXPLANATION
Let's call t to the number of tickets and c to the total cost, the appropiate relationship would be:
c = 2.5t + 10
The variable in the expression represents the number of tickets.
Can I please have help finding the answer? I am really struggling!
Given: An AP whose first term is -20 and a common difference of 3.
Required: To determine the 119th term of the AP.
Explanation: An AP with the first term, a, and with a common difference, d, is of the form-
[tex]a,a+d,a+2d,...,a+(n-1)d[/tex]where n is the number of terms in the AP.
The following formula gives the nth term of the AP-
[tex]a_n=a+(n-1)d[/tex]Here it is given that-
[tex]\begin{gathered} a=-20 \\ d=3 \\ n=19 \end{gathered}[/tex]Substituting these values into the formula for nth terms as-
[tex]a_{19}=-20+(19-1)3[/tex]Further solving-
[tex]\begin{gathered} a_{19}=-20+54 \\ =34 \end{gathered}[/tex]Final Answer: The 19th term of the AP is 34.
Write an absolute value inequality that represents all real numbers more than 4 units away from x
We have to write as inequality the following
"All real numbers more than 4 units away from x""4 units away from x" means four units plus x. So, the expression would be
[tex]|x|>4[/tex]Where x represents real numbers.
This expression is referring to all real numbers more than 4 units and less than -4 units because according to the property of absolute values for inequalities, we have
[tex]|x|>x-4\rightarrow x>x-4,or,x<-(x-4)[/tex]This is represented in the following graph to see it better
For x=1
[tex]\begin{gathered} |1|>x-4\rightarrow1>1-4,or,1<-(1-4) \\ 1>-3 \\ 1<3 \end{gathered}[/tex]Both results are true.
To find this absolute value inequality we used the following property
[tex]|x|>a\rightarrow a>b,or,a<-b[/tex]Where the absolute value inequality has "more than" we rewrite the expression in two inequalities.
Which of the following is an equation of a line that is parallel to y = 4x - 5 and has a y-intercept of (0, 7)?
Answer:
Step-by-step explanation:
To start your equation is in the format y=mx+b.
For a line to be parallel it must have the same slope (m) so we know 4 must remain the same. x & y will not change since they represent the variables. y=4x (so far) then the point (0,7) as stated is the y intercept. 0 is the x value and 7 is the y we need to add 7 to our equation.
final equation y=4x+7
In parallelogram PQRS, diagonals PR and QS intersect at point T.Which statement would prove PQRS is a rhombus?PT > QTPT QTPR QSSTQT
We can have more arguments to prove that PQRS is a rhombus, but, the argument that we will use here is:
Let's look at the first statement, we have
[tex]PT>QT[/tex]That's not correct, it would just prove that QR/2 > PS/2,
[tex]PR=QS[/tex]This statement implies
[tex]\begin{gathered} PR^2=QS^2 \\ \\ PS^2+SR^2=PQ^2+QR^2 \end{gathered}[/tex]We cannot conclude that
[tex]PS=SR=PQ=QR[/tex]The next statement is
[tex]PT=QT[/tex]A rhombus can have different diagonals, and in fact they have. Then let's go to the next one
[tex]ST=QT[/tex]That also not exactly says it's a rhombus, it's a pallelogram property.
[tex]\angle SPT=\angle QPT[/tex]By doing that we have that the diagonal bissects the angle
That implies that the angle b is also bissect.
The last statment is
[tex]\angle PTQ=\angle STR[/tex]That's literally the vertex angle, it's true always, not only in that case, therefore the only possible answer is
[tex]\angle SPT=\angle QPT[/tex]Pro
Which value of x proves that the two triangles above are similar? 42.7 ft 26.7 ft 10 ft 25.6 ft
Explanation
Step 1
we have two triangles
ACE and BCD
if the triangles are similar, then the ratio of the sides must be the same:
[tex]\begin{gathered} \frac{\text{red line}}{purple\text{ line}}=\frac{blue\text{ line}}{\text{green line}} \\ \text{replacing} \\ \frac{16+x}{32}=\frac{x}{20} \end{gathered}[/tex]Step 2
solve for x
[tex]\begin{gathered} \frac{16+x}{32}=\frac{x}{20} \\ \text{cross multiply} \\ 20(16+x)=32\cdot x \\ 320+20x=32x \\ \text{subtrac 20x in both sides} \\ 320+20x-20x=32x-20x \\ 320=12x \\ \text{divide both sides y 12} \\ \frac{320}{12}=\frac{12x}{12} \\ \text{ x=26.66} \end{gathered}[/tex]rounded
[tex]x=26.7\text{ }[/tex]I hope this helps you
Write the equation of the line with x-intercept -2 and y-intercept -1 in slope-intercept form
The x-intercept of -2 gives us an idea that point (-2,0) if found along the line. The y-intercept of -1, tells us that point (0,-1), this also tells us that b = -1.
Now that we have two points, we can solve for slope m
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{Given two points} \\ (-2,0)\rightarrow(x_1,y_1) \\ (0,-1)\rightarrow(x_2,y_2) \\ \\ \text{Substitute} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-0}{0-(-2)} \\ m=-\frac{1}{2} \end{gathered}[/tex]Now that we have both m and b. Substitute these values to the slope intercept form
[tex]\begin{gathered} \text{Slope intercept form is} \\ y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \\ \\ \text{Substitute the values from before and we get} \\ y=-\frac{1}{2}x-1 \end{gathered}[/tex]Hello, I need some assistance with this homework question please for precalculusHW Q1
To transform a function about the y axis
f(x) becomes f(-x)
y = sqrt( x) +2
To transform replace x with -x
y = sqrt(-x) +2
The 2 is a vertical translation up 2
a teacher asks 15 students to estimate an answer to a question the answers or 1, 5, 5, 6, 7, 8, 10, 12 the correct estimate is 7 the teacher wants to calculate how far of the estimate were by finding the absolute value of the difference between each estimate and the answer which estimate was off by the most
We have the following estimations:
1, 5, 5, 6, 7, 8, 10, 12
The absolute value between each estimate and the answer is calculated as:
Estimate Absolute
Answer value
1 |1-7| = |-6| = 6
5 |5-7| = |-2| = 2
5 |5-7| = |-2| = 2
6 |6-7| = |-1| = 1
7 |7-7| = |0| = 0
8 |8-7| = |1| = 1
10 |10-7| = |3| = 3
12 |12-7| = |5| = 5
So, the estimated answer that was off by the most is 1.
18. The surface area of a cone is 12611 square meters. The diameter of the 5 points cone's circular base is 22 meters. What is the lateral area of the cone? Round your answer to the hundredths place value. * A 1 5 7 1 +/- B 5 -- C С 3 2 6 7 3 +/- D 1 4 7 0 2 7 +/-
data
Area = 126pi m^2
diameter = 22
TA = pi r h + pir^2
126pi = LA + pi(11)^2
LA = 126pi - 121pi
LA = 5pi
Letter B.
Solve system of equations using the method of substitution. Identify wether the system represents parallel, coincident, or parallel lines.5x+2y=167.5x+3y=24
Given
5x+2y=16 ---(1)
7.5x+3y=24 ----(2)
Find
1) value of x and y
2) Type of system
Explanation
From equation (1)
[tex]\begin{gathered} 5x+2y=16 \\ 5x=16-2y \\ x=\frac{16-2y}{5} \end{gathered}[/tex]Putting this value of x in equation 2
[tex]\begin{gathered} 7.5x+3y=24 \\ 7.5(\frac{16-2y}{5})+3y=24 \\ 1.5(16-2y)+3y=24 \\ 24-3y+3y=24 \end{gathered}[/tex]From here we cannot find the values of x and y as 3y and -3y will cancel each other. Hence there is not a particular solution
Checking the type of system
From these equations we get
[tex]\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}[/tex]Therefore the lines are coincident to each other
Therefore the lines have infinte solutions
Final Answer
Therefore the lines have infinte solutions
The lines are coincident to each other
Which expression is equivalent to (xy)z?A (x+y)+zB 2z(xy)C x(yz)D x(y+z)
The expression (xy)z can be simplified as;
[tex]\begin{gathered} (xy)z=xyz \\ \text{Therefore xyz;} \\ xyz=x(yz) \end{gathered}[/tex]The correct answer is option C
Fido ran away from home at a speed of 5 mi/hour. He ran in a straight line. After a while he decided to go back home for dinner so turned around and walked home along the same path he had run on. He walked at 2 mi/hour. The walk home took one hour longer than the run did. How long did Fido run?
Distance = Speed x time
For the run; speed = 5 mi/hr, time = t
For the walk: speed= 2 mi/hr, time = t + 1
Since he walked on a straight line and he returned following the same path
Distance travelled for the run = distance travelled for the walk
Distance for run: 5 x t = 5t
Distance for walk : 2 (t + 1) =2t + 2
Thus , 5t = 2t + 2
5t - 2t = 2
3t = 2
t = 2/3 hour = 2/3 x 60 minutes = 2x 20 = 40 minutes
He took him 40 minutes to run
Given the definitions of f(a) and g(x) below, find the value of (19)( 1),f (x) = x2 + 3x – 11g(x) = 3a + 6
The given functions are,
[tex]\begin{gathered} f(x)=x^2+3x-11_{} \\ g(x)=3x+6 \end{gathered}[/tex]Fog can be determined as,
[tex]\begin{gathered} \text{fog}=f(g(x)) \\ =f(3x+6) \\ =(3x+6)^2+3(3x+6)-11 \\ =9x^2+36+36x+9x+18-11 \\ =9x^2+45x+43 \end{gathered}[/tex]The value of fog(-1) can be determined as,
[tex]\begin{gathered} \text{fog}(-1)=9(-1)^2+45(-1)+43 \\ =9-45+43 \\ =7 \end{gathered}[/tex]Thus, the requried value is 7.
Hello. I would like help with problem. Quick answer is OK.Thank you
not continuous, 2 holes. Option A is correct
Explanations;For a function to be continuous, the left hand limit of a function must be equal to the right hand limit at the point x = a
From the graph shown you can see that the limit of the function from the left is not equal to the limit of the function from the right at x = 0. Therefore, we can conclude that there are discontinuities at x = 0.
You can also see that the function has 2 holes at (0, 0) and (0, -1).
Help me pleaseeee quicklyyyyy
∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
Angles 1,2,7 are the interior angles of a triangle and we know that the sum of all interior angles inside a triangle is 180°.
Therefore, ∠1 + ∠2 + ∠7 = 180°
Given, ∠1 = 70° and ∠2 = 65°
∠7 = 180° - (70 + 65) = 45°
Now, ∠8 = 180 - ∠7 ⇒ ∠8 = 135°
Now, ∠7 = ∠6 (vertical opposite angle) so ∠6 = 45°
∠6 = ∠5 (alternative interior angle) so ∠5 = 45°
Hence "∠6 and ∠5 are alternative interior angle thus the measure of angles ∠5 = 45° , ∠6 = 45° ,∠7 = 45° and ∠8 = 135°".
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Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer.
1. angle j and k.
Due to the Converse of Corresponding Angles Postulate, j || k.
2. Angles 2 and 5 are the alternating inner angles of the lines j and k. Given that angle 2 = angle 5,
The Converse of Alternate Interior Angles Theorem states that j || k.
J || K converse alternative interior angles.
what are parallel angles?similarly
3. angle 3 = angle 10 The exterior angles of the lines l and m, respectively, are angle 3 and angle 10. Since the Converse of Alternate Exterior Angles Theorem states that angle 3= angle 10, l || m.
converse alternative exterior angles l || m.
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You spin the spinner once. What is P(2 or odd)?
Answer:
P(2 or odd)=1
Explanation:
The spinner has 3 parts.
The probability of spinning a 2:
[tex]P(2)=\frac{1}{3}[/tex]The probability of spinning an odd number (1, 3):
[tex]P(\text{odd)}=\frac{2}{3}[/tex]Therefore:
[tex]\begin{gathered} P(2\text{ or odd)=}\frac{1}{3}+\frac{2}{3} \\ =\frac{3}{3} \\ =1 \end{gathered}[/tex]Write the ordered pair with no spaces (x,y) of point C for j(x).
This problem is about functions.
In this case, we don't have function j(x) defined in order to find its ordered pairs.
However, assuming that function j(x) is a function of f(x), we can deduct that points C is
[tex]C(0,0)[/tex]PLEASE HURRY ASAP
Determine which integer in the solution set will make the equation true.
4s − 14 = −6
S: {−1, 0, 1, 2}
The solution of the equation is s=2.
Linear FunctionAn equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+1. Where:
m= the slope. It can be calculated for Δy/Δx .
b= the constant term that represents the y-intercept.
For the given example: m=7and b=1.
For solving this question you should replace x for the given values ( −1, 0, 1, 2) in the equation 4s − 14 = −6. If you obtain -6, the value of s is a solution.
For s= -1 -> 4*(-1)-14= -4 -14= -20. Therefore, s=-1 is not the solution.
For s= 0 -> 4*(0)-14= 0 -14= -14. Therefore, s=0 is not the solution.
For s= 1 -> 4*(1)-14= 4 -14= -10. Therefore, s= 1 is not the solution.
For s= 2 -> 4*(2)-14= 8 -14= -6. Therefore, s=2 is the solution.
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Speeds of Cars (in miles per hour)Intersection 1Intersection 2十十十十18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34• Part 1: Find the range of intersection 1 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)• Part 2: Find the range of intersection 2 as a way to measure the variability of the data, showing your work. Remember, range isfound by taking the largest value minus the smallest value. (2 points)
PART 1)
Range of intersection 1
(Max value - Min value )=
Largest value = 31 , Lowest value = 26
Then range1 is 31 - 26 = 5 miles /hour
Now PART 2:)
Maximum value= 27
Minimum value = 22
Then range2 is 27-22 = 5 miles/hour
Covert the decimal into a fraction and reduce to the lowest terms
Solution
- The number given to us can be rewritten as follows:
[tex]92.698=92+0.698[/tex]- Thus, we already know what is in the whole number bracket; 92.
- The fraction representation of 0.698 is what will occupy the fraction brackets.
- 0.698 can be rewritten as:
[tex]0.698=\frac{698}{1000}[/tex]- Let us simplify this fraction as follows:
[tex]\begin{gathered} \frac{698}{1000}=\frac{349\times2}{500\times2} \\ \\ 2\text{ crosses out.} \\ \\ =\frac{349}{500} \end{gathered}[/tex]- Thus, the answer is
Pablo Is choosing at random from a bag of colored marbles. The probability he will choose a red marble is1/9What are the odds in favor of him choosing a redmarble?
Given:
[tex]\text{The probability to choose a red marble=}\frac{1}{9}[/tex]The odds in favour of Pablo chosing a re marble is 1 : 8
8 O 6 4. N Which function is graphed? 2. 4 6 8 -8 -6 -4 -2 0 -2 -6 O A. Y- (x² + 4, x=2 1-x+4,452 (x² + 4, x2 OD. V- x + 4, x32 1-x+4,4
The given curve is parabola and its last point is on the x axis at x = 2
So, the equation of curve is :
[tex]x^2+4,x<2[/tex]In the equation of line,
The line start from x = 2 so, x ≥ 2
So, Equation of line is : -x + 4, x ≥ 2
Answer : B)
[tex]y=\begin{cases}x^2+4,x<2 \\ \square \\ -x+4,\text{ x}\ge2\end{cases}[/tex]Substitute the given values into the given formula and alone the unknown variable if necessary round to one decimal place
c = 15
Explanation:The perimter, P = 37
The side lengths of the triangle are:
a = 10, b = 12, c = ?
The perimeter of the triangle is given by the formula:
P = a + b + c
Substitute a = 10, b = 12, and P = 37 into the formula P = a + b + c and solve for c
37 = 10 + 12 + c
37 = 22 + c
c = 37 - 22
c = 15
Writing the equation of the line through two given points(1,-3) (5,-1). y=mx+b form
Given points (1,-3) and (5,-1).
Since the slope of the line passing through two points
[tex](x_1,y_1)(x_2,y_2)[/tex]The slope of the equation is
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-3)}{5-1} \\ m=\frac{2}{4} \\ m=\frac{1}{2} \end{gathered}[/tex]Therefore, the slope of the line is 1/2.
Now, use the slope and the point (1,-3) to find the y-intercept.
[tex]\begin{gathered} y=mx+c \\ -3=\frac{1}{2}\times1+c \\ c=-3-\frac{1}{2} \\ c=-\frac{-7}{2} \end{gathered}[/tex]Write the equation in slope-intercept form as
[tex]\begin{gathered} y=mx+c \\ y=\frac{1}{2}x-\frac{7}{2} \end{gathered}[/tex]How do I solve this and what is the answer
Answer:
157.5°
Explanation:
To convert from radians to degrees, multiply the angle in radians by 180/π.
Therefore, 7π/8 radians in degrees will be:
[tex]\begin{gathered} \frac{7\pi}{8}\text{ radians=}\frac{7\pi}{8}\times\frac{180}{\pi} \\ =\frac{7}{8}\times180 \\ =157.5\degree \end{gathered}[/tex]help meeeeeeeeee pleaseee !!!!!
The values of the functions evaluated are:
a. (f + g)(x) = 9x + 1
b. (f + g)(x) = -7x + 1
c. (f * g)(x) = 8x² - 55x - 72
d. (f/g)(x) = (x - 8)/(8x + 9)
How to Evaluate Functions?To evaluate a function expression, we are to input the given value of x and solve by combining like terms and simplifying to find the value of the given function expression.
Given the functions:
f(x) = x - 8
g(x) = 8x + 9
a. Find (f + g)(x): This implies that we are to add the two functions f(x) and g(x) together.
(f + g)(x) = x - 8 + 8x + 9
(f + g)(x) = 9x + 1
b. Find (f - g)(x): This implies that we are to subtract g(x) from f(x).
(f - g)(x) = x - 8 - 8x + 9
(f + g)(x) = -7x + 1
c. Find (f * g)(x): This implies that we are to multiply the functions, g(x) and f(x) together.
(f * g)(x) = (x - 8) * (8x + 9)
(f * g)(x) = 8x² - 55x - 72
d. Find (f/g)(x): This implies that we are to find the quotient of the functions, f(x) and g(x).
(f/g)(x) = (x - 8)/(8x + 9)
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Question 8 of 10According to this diagram, what is tan 62°?
In this problem, we want to determine tangent of 62 degrees.
Recall the identity of tangent:
[tex]\tan\theta=\frac{\text{ opposite side}}{\text{ adjacent side}}[/tex]We are given the triangle:
Since we are referencing 62 degrees, the arrow pointing away from the 62 degrees is headed toward the opposite side. Therefore, the opposite side is 15, and the adjacent side is 8.
[tex]\tan62=\frac{15}{8}[/tex]Tangent of 62 degrees is 15/8.